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2013-02-19

Number of Returning POWs

I finally managed to compare the list
of 18,420 Italian POWs with the list of 203,813 people who arrived in
Australia via Fremantle (WA) or transited there on their way to one
of the Eastern ports.

I found 554 entries with matching
family and given names.

I had actually expected a higher number
of matches. Desmond O’Connor,
professor of Italian at Flinders University (Adelaide), in his
article From Tobruk to Clare: the experiences of the Italian
prisoner of war Luigi Bortolotti 1941-1946, which you can read online or download in PDF format,
estimates that 9.4% of Italian POWs held in South Australia returned
to Australia as migrants.

If we assume that the same percentage
applies to POWs held in all states, we arrive to a figure of about
1,700 returnees (9.4% * 18,420 = 1,731). Further, if we assume, as
it seems reasonable to do, that many independent factors influenced the
decision to return to Australia, we can apply the
Central Limit Theorem (CLT) to estimate the degree
of approximation of the mean.

The CLT, for those who are not familiar
with it, states that the mean of a sufficiently large number of
independent random variables is normally distributed. In practical
terms, it means that if we repeatedly measure something that depends
on many independent factors and make a histogram of the values we
measure, the plot will approximate the familiar bell shape of a
normal distribution (thanks to Wikimedia Commons for the following image).

With a normal distribution, we can
roughly estimate its standard deviation (indicated with the Greek
letter σ in the figure) by taking the square root of its mean. In
practical terms, it means that with a mean of 1,731, the standard
deviation of the number of returning POWs nationwide is 42. This in
turn tells us that, according to O’Connor’s estimate, the actual
total number of Italian POWs returning to Australia has a probability
of 68% to be between 1,689 and 1,773. And the probability of the
actual number being less than 1,605 (3σ below the mean) is less than
1%.

My figure of 554 is so low as to be
incompatible with O’Connor’s estimate. Now I have to figure out whether one of us is completely off the mark and why...